Question

The radius of a sphere (in cm) whose volume is \(36 \pi \text{ cm}^{3}\), is :

• A. 3
• B. \(3\sqrt{3}\)
• C. \(3^{\frac{2}{3}}\)
• D. \(3^{\frac{1}{3}}\)

Hint:

Keep an eye out for perfect cubes like 1, 8, 27, 64 in these problems. Once you reach \(r^{3} = 27\), it is easy to see the answer is 3.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Volume of a sphere is a function of its radius \(r\). Given the volume, we can solve for \(r\).
Step 2: Key Formula or Approach:
\[ \text{Volume of Sphere } V = \frac{4}{3} \pi r^{3} \]
Step 3: Detailed Explanation:
Given \(V = 36 \pi\).
Set the formula equal to the given value:
\[ \frac{4}{3} \pi r^{3} = 36 \pi \]
Divide both sides by \(\pi\):
\[ \frac{4}{3} r^{3} = 36 \]
Isolate \(r^{3}\):
\[ r^{3} = 36 \times \frac{3}{4} \]
\[ r^{3} = 9 \times 3 = 27 \]
Take the cube root of both sides:
\[ r = \sqrt[3]{27} = 3 \]
Step 4: Final Answer:
The radius of the sphere is 3 cm.